Network echo cancellation problems are characterized by long echo path impulse responses of the order of 128 ms, of which only a small portion (4-22 ms) is actually nonzero. Adaptive echo cancellers are designed to synthesize the full length of the echo path because (i) the location of the nonzero portion of the echo path (the flat delay) is unknown and (ii) the flat delay varies from call to call. The flat delay is due to the long distance between the echo canceller and the hybrid/local-loop circuit.
A recently proposed modification of NLMS—the Proportionate Normalized Least-Mean-Squares (PNLMS) algorithm (see D. L. Duttweiler, “Proportionate Normalized Least-Mean-Squares Adaption in Echo Cancelers,” IEEE Trans. of Speech and Audio Processing, vol. 8, no. 5, pp. 508-518, September 2000 and S. L. Gay, “An Efficient, Fast Converging Adaptive Filter for Network Echo Cancellation,” in Proc. ASILOMAR, November 1998, pp. 394-398)—exploits the sparseness of the echo path impulse response to speed up the initial convergence of the conventional NLMS algorithm. PNLMS essentially adapts the nonzero portion of the echo path by weighting the update terms of the adaptive filter with the magnitude of the estimated echo path impulse response. This effectively results in a shorter adaptive filter that converges faster than the full-length adaptive filter. The key to PNLMS is the introduction of weighting for adaptive filter coefficients. A particular choice for the weighting gives rise to PNLMS.
There are some disadvantages to PNLMS, namely, an increase in computational complexity by 50% and the slow convergence of the adaptive filter coefficients after the fast initial convergence. The latter is due to the slow convergence of small coefficients after the convergence of the large coefficients over the “active” portion of the echo path impulse response.